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Copy file name to clipboardExpand all lines: _sources/assignments/Assignment_1:Hopfield_Networks/README.md
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#### Visualization 2
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Plot the expected number of accurately retrieved memories vs. network size.
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Let:
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- $P[m, N] \in [0, 1]$: proportion of $m$ memories accurately retrieved in a network of size $N$
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- $\mathbb{E}[R_N]$: expected number of successfully retrieved memories
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Then:
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$$
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\mathbb{E}[R_N] = \sum_{m=1}^{M} m \cdot P[m, N]
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$$
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Where $M$ is the maximum number of memories tested.
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Plot the estimated number of accurately retrieved memories as a function of network size.
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You can use the heatmap you made above to estimate the number of accurately retrieved memories:
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- Choose a target proportion (e.g., $p = 0.8$ or similar)
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- For each network size you tested to make your heatmap, compute the maximum number of memories for which at least proportion $p$ were successfully retrieved
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#### Follow-Up
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- What relationship (if any) emerges between network size and capacity?
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- Can you develop rules or intuitions that help predict a network’s capacity?
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- Hint: see page 3 of [Amit et al. (1985)](https://www.dropbox.com/scl/fi/3a3adwqf70afb9kmieezn/AmitEtal85.pdf?rlkey=78fckvuuvk9t3o9fbpjrmn6de)
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---
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Context drift:
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- Set $\text{context}^1$ randomly
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- For each subsequent $\text{context}^{t+1}$, copy $\text{context}^t$ and flip ~5% of the bits
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- For each subsequent $\text{context}^{t+1}$, copy $\text{context}^t$ and flip ~10% of the bits
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#### Simulation Procedure
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- Set item neurons to 0
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- Run until convergence
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- For each stored memory $j$, compare recovered item to $\text{item}^j$
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- If ≥99% of bits match, record $j$ as retrieved
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- If ≥75% of bits match, record $j$ as retrieved
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- Record $\Delta = j - i$ (relative offset)
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#### Analysis
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- Repeat the procedure (e.g., 100 trials)
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- Repeat the procedure (e.g., 100 trials). Note that you will need to "reset" the network (i.e., start with an empty weight matrix and re-encode the 10 memories) each time you repeat the simulation.
Copy file name to clipboardExpand all lines: _sources/assignments/Assignment_2:Search_of_Associative_Memory_Model/README.md
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# Assignment 2: Search of Associative Memory (SAM) Model
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## Overview
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In this assignment, you will implement the **Search of Associative Memory (SAM) model** as described in [Atkinson & Shiffrin (1968)](https://www.dropbox.com/scl/fi/rpllozjcv704okckjdy5k/AtkiShif68.pdf?rlkey=i0azhj9mqxws7bxocbl65j88d&dl=1). The SAM model is a probabilistic model of free recall that assumes items are stored in **short-term memory (STS)** and **long-term memory (LTS)**, with retrieval governed by associative processes. You will fit your implementation to [Murdock (1962)](https://www.dropbox.com/scl/fi/k7jc1b6uua4m915maglpl/Murd62.pdf?rlkey=i5nc7lzb2pw8dxc6xc72r5r5i&dl=1) free recall data and evaluate how well the model explains the observed recall patterns.
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In this assignment, you will implement the **Search of Associative Memory (SAM) model** as described in [Kahana (2012), Chapter 7](https://www.dropbox.com/scl/fi/ujl8yvxqzcb1gf32to4zb/Kaha12_SAM_model_excerpt.pdf?rlkey=254wtw4fm7xnpzelno2ykrxzu). The SAM model is a probabilistic model of free recall that assumes items are stored in **short-term memory (STS)** and **long-term memory (LTS)**, with retrieval governed by associative processes. You will fit your implementation to [Murdock (1962)](https://www.dropbox.com/scl/fi/k7jc1b6uua4m915maglpl/Murd62.pdf?rlkey=i5nc7lzb2pw8dxc6xc72r5r5i&dl=1) free recall data and evaluate how well the model explains the observed recall patterns.
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## Data Format and Preprocessing
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The dataset consists of sequences of recalled items from multiple trials of a free recall experiment. Each row represents a participant’s recall sequence from a single list presentation.
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## Model Description
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*NOTE: NEED TO UPDATE THIS!!! Don't start this assignment quite yet...*
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You will implement and fit a **Search of Associative Memory (SAM)** model that consists of:
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### 1. **Encoding Stage: Memory Storage**
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- Identifies strengths and weaknesses of SAM.
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## Submission Instructions
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- Submit a **Google Colaboratory notebook** (or similar) that includes:
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-[Submit](https://canvas.dartmouth.edu/courses/71051/assignments/517354) a **Google Colaboratory notebook** (or similar) that includes:
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- Your **full implementation** of the SAM model.
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-**Markdown cells** explaining your code, methodology, and results.
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-**All required plots** comparing model predictions to observed data.
Copy file name to clipboardExpand all lines: assignments/Assignment_1:Hopfield_Networks/README.html
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</section>
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<sectionid="visualization-2">
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<h4>Visualization 2<aclass="headerlink" href="#visualization-2" title="Link to this heading">#</a></h4>
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<p>Plot the expected number of accurately retrieved memories vs. network size.</p>
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<p>Let:</p>
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<p>Plot the estimated number of accurately retrieved memories as a function of network size.
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You can use the heatmap you made above to estimate the number of accurately retrieved memories:</p>
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<ulclass="simple">
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<li><p><spanclass="math notranslate nohighlight">\(P[m, N] \in [0, 1]\)</span>: proportion of <spanclass="math notranslate nohighlight">\(m\)</span> memories accurately retrieved in a network of size <spanclass="math notranslate nohighlight">\(N\)</span></p></li>
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<li><p><spanclass="math notranslate nohighlight">\(\mathbb{E}[R_N]\)</span>: expected number of successfully retrieved memories</p></li>
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<li><p>Choose a target proportion (e.g., <spanclass="math notranslate nohighlight">\(p = 0.8\)</span> or similar)</p></li>
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<li><p>For each network size you tested to make your heatmap, compute the maximum number of memories for which at least proportion <spanclass="math notranslate nohighlight">\(p\)</span> were successfully retrieved</p></li>
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</ul>
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<p>Then:</p>
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<divclass="math notranslate nohighlight">
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\[
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\mathbb{E}[R_N] = \sum_{m=1}^{M} m \cdot P[m, N]
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\]</div>
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<p>Where <spanclass="math notranslate nohighlight">\(M\)</span> is the maximum number of memories tested.</p>
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</section>
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<sectionid="follow-up">
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<h4>Follow-Up<aclass="headerlink" href="#follow-up" title="Link to this heading">#</a></h4>
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<ulclass="simple">
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<li><p>What relationship (if any) emerges between network size and capacity?</p></li>
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<li><p>Can you develop rules or intuitions that help predict a network’s capacity?</p></li>
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<li><p>Hint: see page 3 of <aclass="reference external" href="https://www.dropbox.com/scl/fi/3a3adwqf70afb9kmieezn/AmitEtal85.pdf?rlkey=78fckvuuvk9t3o9fbpjrmn6de">Amit et al. (1985)</a></p></li>
<li><p>For each subsequent <spanclass="math notranslate nohighlight">\(\text{context}^{t+1}\)</span>, copy <spanclass="math notranslate nohighlight">\(\text{context}^t\)</span> and flip ~5% of the bits</p></li>
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<li><p>For each subsequent <spanclass="math notranslate nohighlight">\(\text{context}^{t+1}\)</span>, copy <spanclass="math notranslate nohighlight">\(\text{context}^t\)</span> and flip ~10% of the bits</p></li>
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</ul>
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</section>
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<sectionid="id4">
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<li><p>Set item neurons to 0</p></li>
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<li><p>Run until convergence</p></li>
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<li><p>For each stored memory <spanclass="math notranslate nohighlight">\(j\)</span>, compare recovered item to <spanclass="math notranslate nohighlight">\(\text{item}^j\)</span></p></li>
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<li><p>If ≥99% of bits match, record <spanclass="math notranslate nohighlight">\(j\)</span> as retrieved</p></li>
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<li><p>If ≥75% of bits match, record <spanclass="math notranslate nohighlight">\(j\)</span> as retrieved</p></li>
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<sectionid="id5">
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<h4>Analysis<aclass="headerlink" href="#id5" title="Link to this heading">#</a></h4>
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<ulclass="simple">
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<li><p>Repeat the procedure (e.g., 100 trials)</p></li>
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<li><p>Repeat the procedure (e.g., 100 trials). Note that you will need to “reset” the network (i.e., start with an empty weight matrix and re-encode the 10 memories) each time you repeat the simulation.</p></li>
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<li><p>For each <spanclass="math notranslate nohighlight">\(\Delta \in [-9, +9]\)</span>, compute:</p>
Copy file name to clipboardExpand all lines: assignments/Assignment_2:Search_of_Associative_Memory_Model/README.html
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<h1>Assignment 2: Search of Associative Memory (SAM) Model<aclass="headerlink" href="#assignment-2-search-of-associative-memory-sam-model" title="Link to this heading">#</a></h1>
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<sectionid="overview">
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<h2>Overview<aclass="headerlink" href="#overview" title="Link to this heading">#</a></h2>
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<p>In this assignment, you will implement the <strong>Search of Associative Memory (SAM) model</strong> as described in <aclass="reference external" href="https://www.dropbox.com/scl/fi/rpllozjcv704okckjdy5k/AtkiShif68.pdf?rlkey=i0azhj9mqxws7bxocbl65j88d&amp;dl=1">Atkinson & Shiffrin (1968)</a>. The SAM model is a probabilistic model of free recall that assumes items are stored in <strong>short-term memory (STS)</strong> and <strong>long-term memory (LTS)</strong>, with retrieval governed by associative processes. You will fit your implementation to <aclass="reference external" href="https://www.dropbox.com/scl/fi/k7jc1b6uua4m915maglpl/Murd62.pdf?rlkey=i5nc7lzb2pw8dxc6xc72r5r5i&amp;dl=1">Murdock (1962)</a> free recall data and evaluate how well the model explains the observed recall patterns.</p>
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<p>In this assignment, you will implement the <strong>Search of Associative Memory (SAM) model</strong> as described in <aclass="reference external" href="https://www.dropbox.com/scl/fi/ujl8yvxqzcb1gf32to4zb/Kaha12_SAM_model_excerpt.pdf?rlkey=254wtw4fm7xnpzelno2ykrxzu">Kahana (2012), Chapter 7</a>. The SAM model is a probabilistic model of free recall that assumes items are stored in <strong>short-term memory (STS)</strong> and <strong>long-term memory (LTS)</strong>, with retrieval governed by associative processes. You will fit your implementation to <aclass="reference external" href="https://www.dropbox.com/scl/fi/k7jc1b6uua4m915maglpl/Murd62.pdf?rlkey=i5nc7lzb2pw8dxc6xc72r5r5i&amp;dl=1">Murdock (1962)</a> free recall data and evaluate how well the model explains the observed recall patterns.</p>
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</section>
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<sectionid="data-format-and-preprocessing">
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<h2>Data Format and Preprocessing<aclass="headerlink" href="#data-format-and-preprocessing" title="Link to this heading">#</a></h2>
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</section>
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<sectionid="model-description">
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<h2>Model Description<aclass="headerlink" href="#model-description" title="Link to this heading">#</a></h2>
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<p><em>NOTE: NEED TO UPDATE THIS!!! Don’t start this assignment quite yet…</em></p>
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<p>You will implement and fit a <strong>Search of Associative Memory (SAM)</strong> model that consists of:</p>
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<sectionid="encoding-stage-memory-storage">
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<h3>1. <strong>Encoding Stage: Memory Storage</strong><aclass="headerlink" href="#encoding-stage-memory-storage" title="Link to this heading">#</a></h3>
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<sectionid="submission-instructions">
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<h2>Submission Instructions<aclass="headerlink" href="#submission-instructions" title="Link to this heading">#</a></h2>
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<ulclass="simple">
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<li><p>Submit a <strong>Google Colaboratory notebook</strong> (or similar) that includes:</p>
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<li><p><aclass="reference external" href="https://canvas.dartmouth.edu/courses/71051/assignments/517354">Submit</a> a <strong>Google Colaboratory notebook</strong> (or similar) that includes:</p>
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<ul>
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<li><p>Your <strong>full implementation</strong> of the SAM model.</p></li>
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<li><p><strong>Markdown cells</strong> explaining your code, methodology, and results.</p></li>
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